Document information is already available, even if a bit hidden. You can open the menu in the top right of the PDF viewer, and select Document properties.
It doesn't currently contain font information because it's not really user facing information. We could consider adding it if it would be widely useful.
@marco, Yes I am aware of the document information that is already available. I don't think it is too hidden because I had no problem finding it. But unfortunately it doesn't list the fonts.
If you see a font that you are curious about, this would be useful in finding out what that font it. It would also be useful when you have generated a PDF and want to inspect it and to figure out which fonts are included, and figure out if your font you wanted isn't included. To figure out if some backup or substitute font is used instead, to figure out if its a default font or an embedded one and such.